4 papers
Dynamics of composite symplectic Dehn twists
Wenmin Gong, Zhijing Wendy Wang, Jinxin Xue
This paper appears as the confluence of hyperbolic dynamics, symplectic topology and low dimensional topology, etc. We show that composite symplectic Dehn twists have certain form…
On Aubry's completeness conjecture
Tianqi Shi, Jinxin Xue
In this paper, we prove Aubry's completeness stating conjecture that for a twist map the graph of rotation numbers as a function of the cohomology classes is a purely singularly co…
Generic mean curvature flows with cylindrical singularities I: the normal forms and nondegeneracy
Ao Sun, Jinxin Xue
This paper studies the dynamics of mean curvature flow as it approaches a cylindrical singularity. We proved that the rescaled mean curvature flow converging to a smooth generalize…
Generic Dynamics of Mean Curvature Flows with Asymptotically Conical Singularities
Ao Sun, Jinxin Xue
This is the second paper in the series to study the generic dynamics of mean curvature flows. We study the initial perturbation of mean curvature flows, whose first singularity is…